Weird artifacts in my UV mapped texture
Remove doubles in the mesh

What happens in your mesh now is  Z-fighting. Notice the clipping while rotating view around the barrel:



While in Edit mode select all and press W > Remove Doubles. It will delete ~800 double vertices. 

After that you can split normals either by adding Edge Split modifier or activating Auto Smooth in Object Data tab.

Also see:

Overlapping faces:

Cause of black artifacts in render?

Overlapping faces in mirror modifier causing z-fighting

Edge Split modifier vs. Auto Smooth:

How to smooth shade an object while retaining hard edges?